Experimental analysis of driveline shuffle with focus on the interaction between traction and torsional vibrations ⁎

9th IFAC International Symposium on Advances in Automotive 9th 9th IFAC IFAC International International Symposium Symposium on on Advances Advances in in Automotive Automotive Control 9th IFAC International Symposium onAvailable Advancesonline in Automotive Control at www.sciencedirect.com Control Orléans, France, June 23-27, 2019 9th IFAC International Symposium on Advances in Automotive Control Orléans, Orléans, France, France, June June 23-27, 23-27, 2019 2019 Control Orléans, France, June 23-27, 2019 Orléans, France, June 23-27, 2019

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IFAC PapersOnLine 52-5 (2019) 322–328

Experimental analysis of driveline shuffle Experimental analysis of driveline shuffle Experimental analysis of driveline shuffle Experimental analysis of driveline shuffle with focus on the interaction between Experimental analysis of driveline shuffle with focus on the interaction between with focus on the interaction between  with focus on the interaction between traction and torsional vibrations with focus on the interaction between  traction and torsional vibrations traction traction and and torsional torsional vibrations vibrations  traction torsional vibrations ∗ ∗∗ Korbinian and J. Figel ∗ Matthias Schultalbers ∗∗

Korbinian J. Figel ∗ Matthias Schultalbers ∗∗ ∗∗∗ Korbinian Figel ∗∗ Ferdinand SvaricekSchultalbers ∗∗∗ Korbinian J. J. Figel ∗∗ Matthias Matthias Schultalbers Ferdinand Svaricek ∗∗∗ ∗∗ Ferdinand Svaricek ∗∗∗ Korbinian J. Figel Matthias Schultalbers Ferdinand Svaricek ∗∗∗ ∗ Ferdinand Munich,Svaricek Neubiberg, BY 85577 Germany ∗ Bundeswehr University ∗ Bundeswehr University Munich, Neubiberg, BY 85577 Germany Munich, ∗ Bundeswehr University (e-mail: [email protected]). Bundeswehr University Munich, Neubiberg, Neubiberg, BY BY 85577 85577 Germany Germany (e-mail: [email protected]). ∗ ∗∗ (e-mail: [email protected]). Bundeswehr University Munich, BY 85577 Germany Gifhorn, NI Neubiberg, 38518 Germany (e-mail: ∗∗ IAV GmbH, (e-mail: [email protected]). ∗∗ IAV GmbH, Gifhorn, NI 38518 Germany (e-mail: Gifhorn, NI 38518 Germany (e-mail: ∗∗ IAV GmbH, (e-mail: [email protected]). [email protected]) IAV GmbH, Gifhorn, NI 38518 Germany (e-mail: [email protected]) ∗∗ ∗∗∗ [email protected]) IAV GmbH, Gifhorn, NI 38518 Germany (e-mail: University Munich, Neubiberg, BY 85577 Germany ∗∗∗ Bundeswehr [email protected]) Munich, Neubiberg, BY 85577 Germany ∗∗∗ Bundeswehr University University Munich, Neubiberg, BY 85577 Germany ∗∗∗ Bundeswehr [email protected]) (e-mail: [email protected]) Bundeswehr University Munich, Neubiberg, BY 85577 Germany (e-mail: [email protected]) ∗∗∗ [email protected]) Bundeswehr(e-mail: University Munich, Neubiberg, BY 85577 Germany (e-mail: [email protected]) (e-mail: [email protected]) Abstract: Recent research showed by theoretical analysis a significant role of the interaction Abstract: Recent research showed by theoretical analysis aa significant role of the interaction Abstract: Recent research showed by analysis role of interaction between traction and low-frequency vibrations (known as driveline anti-jerk Abstract: Recent research showed torsional by theoretical theoretical analysis a significant significant roleshuffle) of the the on interaction between traction and low-frequency torsional vibrations (known as driveline shuffle) on anti-jerk between traction and low-frequency torsional vibrations (known as driveline shuffle) on anti-jerk Abstract: Recent research showed by theoretical analysis a significant role of the interaction controller design in passenger cars. This paper addresses the experimental validation of these between traction and low-frequency torsional vibrations (known as driveline shuffle) on anti-jerk paper controller design in passenger cars. This addresses the experimental validation of these controller design in passenger cars. This paper addresses the experimental validation of these between traction and low-frequency torsional vibrations (known as driveline shuffle) on anti-jerk findings in a wide range of operating points. Various experiments have been performed with controller design inrange passenger cars. This paper addresses the experimental validation ofwith theseaa findings in a wide of operating points. Various experiments have been performed findings in a wide range of operating points. Various experiments have been performed with controller design in passenger cars. This paper addresses the experimental validation of theseaa plug-in hybrid electric vehicle. Several excitation amplitudes have been applied at different findings hybrid in a wide rangevehicle. of operating points. Various experiments have been performed with have been applied at different plug-in electric Several excitation amplitudes plug-in hybrid electric vehicle. Several excitation amplitudes have been applied at different findings in a wide range of operating points. experiments have been performed with a vehicle speeds and driving conditions. As aVarious result, the dependency of the driveline shuffle plug-in hybrid electric vehicle. Several excitation amplitudes have been applied at different vehicle speeds and driving conditions. As aa result, the dependency of the driveline shuffle vehicle speeds and driving conditions. As result, the dependency of the driveline shuffle plug-in hybrid electric vehicle. Several excitation amplitudes have been applied at different characteristics is quantified in this study. These results are the first step towards a guideline vehicle speeds is and driving in conditions. AsThese a result, theare dependency of the driveline shuffle characteristics quantified this study. results the first step towards aa guideline characteristics is quantified study. results the step towards vehicle speeds and driving conditions. AsThese a result, theare dependency of the driveline shuffle for control engineers during in thethis model selection process for either anti-jerk controller concept characteristics is quantified in this study. These results are the first first step towards a guideline guideline for control engineers during the model selection process for either anti-jerk controller concept for control engineers during the model selection process for either anti-jerk controller concept characteristics is quantified in this study. These results are the first step towards a guideline design, parametrization or validation. Based on these results a linear parameter varying model for control engineers during the modelBased selection process for either anti-jerk controller concept or validation. design, parametrization on these results aa linear parameter varying model design, or validation. on these results linear parameter varying model for control engineers during the modelBased selection process for either anti-jerk controller concept (LPV) isparametrization proposed. design, parametrization or validation. Based on these results a linear parameter varying model (LPV) is proposed. (LPV) is proposed. design, parametrization or validation. Based on these results a linear parameter varying model (LPV) is proposed. © 2019,isIFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. (LPV) proposed. Keywords: Driveline Modelling, Driveline Dynamics, Model-Based Calibration, Calibration, Drivability Keywords: Driveline Modelling, Driveline Dynamics, Model-Based Calibration, Drivability Keywords: Keywords: Driveline Driveline Modelling, Modelling, Driveline Driveline Dynamics, Dynamics, Model-Based Model-Based Calibration, Drivability Drivability Keywords: Driveline Modelling, Driveline Dynamics, Model-Based Calibration, Drivability 1. INTRODUCTION in-vehicle driving tests (Konig et al. (2014); Pillas (2017)). 1. INTRODUCTION in-vehicle driving tests (Konig et al. (2014); Pillas (2017)). 1. INTRODUCTION in-vehicle driving tests (Konig et al. (2014); Pillas (2017)). Most of the studies focus on controller design methods, 1. INTRODUCTION in-vehicle driving tests (Konig et al. (2014); Pillasmethods, (2017)). Most of the studies focus on controller design Most studies focus on controller design methods, 1. INTRODUCTION in-vehicle driving tests (Konig et al. (2014); Pillas (2017)). based of on the linear time-invariant (LTI) models, identified at Automotive drivelines, either operated with electric drives Most of the studies focus on controller design methods, Automotive drivelines, either operated with electric drives based on linear time-invariant (LTI) models, identified at based on linear time-invariant (LTI) models, identified at Automotive drivelines, either operated with electric drives Most of the studies focus on controller design methods, a single operating point (Grotjahn et al. (2006); Syed et al. (Menne and De Doncker (2000); G¨ o tting and De Doncker based on linear time-invariant (LTI) models, identified at Automotive drivelines, either operated with electric drives (Menne and De Doncker (2000); G¨ o tting and De Doncker a single operating point (Grotjahn et al. (2006); Syed et al. a single operating point (Grotjahn et al. (2006); Syed et al. (Menne and De Doncker (2000); G¨ o tting and De Doncker based on linear time-invariant (LTI) models, identified at (2009); Templin and Egardt (2009); Alt et al. (2011)) Automotive drivelines, either operated with electric drives (2001)) or with combustion engines (Togai et al. (2002); a single operating point (Grotjahn et al. (2006); Syed et al. (Menne and De Doncker (2000); G¨ o tting and De Doncker (2009); Templin and Egardt (2009); Alt et al. (2011)) (2001)) or with combustion engines (Togai et al. (2002); (2009); Templin and Egardt (2009); Alt et al. (2011)) (2001)) or with combustion engines (Togai et al. (2002); a single operating point (Grotjahn et al. (2006); Syed et al. or proving their method with a single experiment (e.g. (Menne and De Doncker (2000); G¨ o tting and De Doncker Bovee (2015)), tend to torsional vibrations during abrupt (2009); Templin and Egardt (2009); Alt et al. (2011)) (2001))(2015)), or withtend combustion engines (Togai during et al. (2002); or proving their method with aa single experiment (e.g. Bovee to torsional vibrations abrupt proving their method with single experiment (e.g. Bovee to vibrations during abrupt (2009); Templin and (2011)). Egardt (2009); et al. (2011)) Angeringer and large parameter (2001)) or with combustion (Togai et al.of(2002); maneuvers. Duetend to the the finiteengines torsional stiffness mate- or or proving theirHorn method withIn acontrast, singleAlt experiment (e.g. Bovee (2015)), (2015)), tend to torsional torsional vibrations during abrupt maneuvers. Due to finite torsional stiffness of mateAngeringer and Horn (2011)). In contrast, large parameter Angeringer and Horn (2011)). In contrast, large parameter maneuvers. Due to the finite torsional stiffness of mateor proving their method with a single experiment (e.g. uncertainties of Horn a linear model have beenlarge reported from Boveeall(2015)), tend to torsional vibrations during abrupt rial, common drivetrain topologies are composed of Angeringer and (2011)). In contrast, parameter maneuvers. Due to the finite torsional stiffness of material, all common drivetrain topologies are composed of uncertainties of aa linear model have been reported from uncertainties of linear model have been reported from rial, all common drivetrain topologies are composed of Angeringer and Horn (2011)). In contrast, large parameter driving-tests in Konig et al. (2014) and effort is made for maneuvers. Due to the finite torsional stiffness of mateelastic parts, suchdrivetrain as drive-shafts, drive-shafts, gear-wheels, clutches uncertainties in of Konig a linear model haveand been reported from rial, allparts, common topologies are composed of driving-tests et al. (2014) effort is made for elastic such as gear-wheels, clutches driving-tests in Konig et al. (2014) and effort is made for elastic parts, such as drive-shafts, gear-wheels, clutches uncertainties of a linear model have been reported from the development of robust control design methods in Pham rial, all common drivetrain topologies are composed of or bearings. Hence, external torques, like the motor or driving-tests in Konig et al. (2014) and methods effort is made for elastic parts, Hence, such asexternal drive-shafts, gear-wheels, clutches or bearings. torques, like the motor or the development of robust control design in Pham the development of robust control design methods in Pham or bearings. Hence, external torques, like the motor or driving-tests in Konig et al. (2014) and effort is made for et al. (2016), order to handle a variation of the system’s elastic parts, such as drive-shafts, gear-wheels, clutches brake torque, can excite vibrations of the drivetrain. With the development of robust control design methods in Pham or bearings. Hence, external torques, like the motor or et al. (2016), in order to handle a variation of the system’s brake torque, can excite vibrations of the drivetrain. With et al. (2016), in order handle aa variation of the system’s brake torque, can excite vibrations of the drivetrain. With development of robust control design inon Pham damping property. Asto these studies aremethods focused the or bearings. Hence, external torques, like the vibrations motor or the increasing excitation torque gradients, these et al. (2016), in order to handle variation of the system’s brake torque, can excite vibrations of the drivetrain. With increasing excitation torque gradients, these vibrations damping property. As these studies are focused on the damping property. As studies are on increasing excitation torque vibrations al. (2016), in order handle a variation ofinvestigations the system’s robustness of the control method, no further brake torque, can excite vibrations the these drivetrain. With et get sensible for the driver andgradients, are of considered uncomfortdamping property. Astothese these studies are focused focused on the the increasing excitation torque gradients, these vibrations robustness of the control method, no further investigations get sensible for the driver and are considered uncomfortrobustness of control method, no investigations get for the the when driver andaccelerator are considered considered uncomfortdamping As these studies are focused the theproperty. origin these parameter deviations are on made. increasing excitation torque gradients, these vibrations able. For example, example, the pedaluncomfortis pressed pressed about robustness of the the of control method, no further further investigations get sensible sensible for driver and are able. For when the accelerator pedal is about the origin of these parameter deviations are made. about the origin of these parameter deviations are made. able. For example, when the accelerator pedal is pressed robustness of the control method, no further investigations There is also a notable diversity in the complexity of modget sensible for the driver and are considered uncomfortquickly, a so-called Tip-In maneuver, a step-like acceleraabout the origin of these parameter deviations are made. able. Fora example, when the accelerator pedal isaccelerapressed There is also a notable diversity in the complexity of modquickly, so-called Tip-In maneuver, a There is aa notable diversity in complexity modquickly, so-called Tip-In maneuver, aa step-like step-like thealso origin these parameter areof els ranging from aofsimple approximation of a second-order able.change Foraa example, when the pedal isaccelerapressed about tion is requested requested of theaccelerator vehicle. This is translated translated There is also notable diversity in the thedeviations complexity ofmade. modquickly, so-called Tip-Inof maneuver, step-like acceleration change is the vehicle. This is els ranging from aa simple approximation of aa second-order els ranging from simple approximation of second-order tion change is requested of the vehicle. This is translated There is also a notable diversity in the complexity of modbehavior (Togai et al. (2002)) to a rather complex multiquickly, a so-called Tip-In maneuver, a step-like accelerato a motor torque by the motor control unit. When this els ranging from a simple approximation of a second-order tion change is requested of the vehicle. This is translated behavior (Togai et al. (2002)) to a rather complex multito aa motor torque by the motor control unit. When this behavior (Togai et al. (2002)) to a rather complex multito motor torque by the motor control unit. When this els ranging from a simple approximation of a second-order body simulation model (H¨ u lsmann (2007)). However, most tion change is requested of the vehicle. This is translated step-like torque is applied to the drivetrain, low-frequency (Togai model et al. (2002)) to a(2007)). rather complex multito a motor torque by the to motor control unit. When this behavior step-like torque is applied the drivetrain, low-frequency body simulation (H¨ u lsmann However, most body simulation model (H¨ u lsmann (2007)). However, most step-like torque is applied to the drivetrain, low-frequency behavior (Togai et al. (2002)) to a rather complex multiof the authors basically use a pure rotational model of two to a motor torque by the motor control unit. When this vibrations occur which are known as driveline shuffle. A body simulation model (H¨ u lsmann (2007)). However, most step-like torque iswhich applied toknown the drivetrain, low-frequency vibrations occur are as driveline shuffle. A of the authors basically use a pure rotational model of two of the authors basically use a pure rotational model of two vibrations occur which are known as driveline shuffle. A body simulation model (H¨ u lsmann (2007)). However, most inertias coupled by a linear spring and damper in parallel step-like torque iswhich applied toknown the drivetrain, low-frequency suitable motor-management is able to modify the motor of the authors basically use a pure rotational model of two vibrations occur are as driveline shuffle. A suitable motor-management is able to modify the motor inertias coupled by a linear spring and damper in parallel inertias coupled by a linear spring and damper in parallel suitable motor-management is able to modify the motor of the authors basically use a pure rotational model of two to catch the main dynamics (e.g. Grotjahn et al. (2006)). vibrations occur which are known as driveline shuffle. A torque such that the requested change of acceleration is inertias coupled by a linear spring and damper in parallel suitable motor-management is able to modify the motor to catch the main dynamics (e.g. Grotjahn et al. (2006)). torque such that the requested change of acceleration is to catch the main dynamics (e.g. Grotjahn et al. (2006)). torque such that the requested change of acceleration is inertias coupled by a linear spring and damper in parallel Often, this ’two-inertias model’ is complemented by adsuitable motor-management is able to modify the motor reached as fast as possible, while the sensible drivetrain vicatchthis the’two-inertias main dynamics (e.g.isGrotjahn et al. (2006)). torque such that the requested change of acceleration is to reached as fast as possible, while the sensible drivetrain viOften, model’ complemented by adOften, this ’two-inertias model’ is complemented by adreached as fast as possible, while the sensible drivetrain vito catch the main dynamics (e.g. Grotjahn et al. (2006)). ditional effects. Some authors focus on backlash handling torque such that the requested change of acceleration is brations (0 Hz to 10 Hz ISO 2631 (1997); ISO 8041 (2005)) Often, this ’two-inertias model’ is complemented by adreached as fast as 10 possible, while the sensible drivetrain vi- ditional effects. Some authors focus on backlash handling brations (0 Hz to Hz ISO 2631 (1997); ISO 8041 (2005)) ditional effects. Some authors focus on backlash handling brations (0 Hz to 10 Hz ISO 2631 (1997); ISO 8041 (2005)) Often, this ’two-inertias model’ is complemented by ad(Caruntu and Lazar (2012); Lagerberg and Egardt (2004)), reached as fast as possible, while the sensible drivetrain viare reduced sufficiently. This trade-off between a fast sysditional effects. Some authors focus on backlash handling brations (0 Hz to 10 Hz ISO 2631 (1997); ISO 8041 (2005)) are reduced sufficiently. This trade-off between a fast sys(Caruntu and Lazar (2012); Lagerberg and Egardt (2004)), (Caruntu and Lazar (2012); Lagerberg and Egardt (2004)), are reduced sufficiently. This trade-off between a fast sysditional effects. Some authors focus on backlash handling whereas other include the elastic behavior of the clutch brations (0 Hz to 10 Hz ISO 2631 (1997); ISO 8041 (2005)) tem response and comfort is called drivability. There are (Caruntu and Lazar (2012); Lagerberg and Egardt (2004)), are reduced sufficiently. This trade-off between aThere fast syswhereas other include the elastic behavior of the clutch tem response and comfort is called drivability. are other include the elastic behavior of the clutch tem response and comfort is called are (Caruntu and (2012); Lagerberg and Egardt (2004)), (Grotjahn et Lazar al. (2006); (2005)) the dual are sufficiently. between fast sysnumerous studies on theThis model-based design of ofaThere these so- whereas whereas other include theSchwenger elastic behavior ofor the clutch temreduced response and on comfort is trade-off called drivability. drivability. There are numerous studies the model-based design these so(Grotjahn et al. (2006); Schwenger (2005)) or the dual (Grotjahn et al. (2006); Schwenger (2005)) or the dual numerous studies on the model-based design of these sowhereas other include the elastic behavior of the clutch mass flywheel (Walter (2008)). Others also or include tire tem response and comfort isHowever, called drivability. There are called anti-jerk controllers. the parametrization (Grotjahn et al. (2006); Schwenger (2005)) the dual numerous studies on the model-based design of these socalled anti-jerk controllers. However, the parametrization mass flywheel (Walter (2008)). Others also include tire mass flywheel (Walter (2008)). Others also include tire called anti-jerk controllers. However, the parametrization (Grotjahn et al. (2006); Schwenger (2005)) or the dual properties. The tire models range from a kinematic relanumerous studies on the model-based design of these soof these control functions is still mostly done in laborious mass flywheel (Walter (2008)). Others also include tire called anti-jerk controllers. However, the parametrization properties. The tire models range from a kinematic relaof these control functions is still mostly done in laborious properties. The tire models range from a kinematic relaof these control functions is still mostly done in laborious mass flywheel (Walter (2008)). Others also include tire tionship between the wheel rotation and the longitudinal called anti-jerk controllers. However, the parametrization properties. The tire models range from a kinematic relaof these control functions is still mostly done in laborious tionship between the wheel rotation and the longitudinal  This work was partly funded by the IAV GmbH Ingenieurgetionship between the wheel rotation and the longitudinal properties. The tire models range from a kinematic reladisplacement of the vehicle (Baumann et al. (2006)) to a of these control functions is still mostly done in laborious  tionship between the wheel rotation and the longitudinal This was partly funded by GmbH Ingenieurge displacement of the et al. (2006)) to a This work work funded by the the IAV IAV GmbH Ingenieurgesellschaft Autowas undpartly Verkehr, Carnotstraße 1, 10587 Berlin.  displacement of the vehicle (Baumann et al. (2006)) to a tionship between thevehicle wheel (Baumann rotation and the longitudinal This work was partly funded by the IAV GmbH Ingenieurgedisplacement of the vehicle (Baumann et al. (2006)) to a sellschaft Auto und Verkehr, Carnotstraße 1, 10587 Berlin.  sellschaft Auto und Verkehr, Carnotstraße 1, 10587 Berlin. This work funded by the IAV GmbH Ingenieurgedisplacement of the vehicle (Baumann et al. (2006)) to a sellschaft Autowas undpartly Verkehr, Carnotstraße 1, 10587 Berlin.

sellschaft und Verkehr, Carnotstraße 1, 10587 Berlin. 2405-8963Auto © 2019 2019, IFAC (International Federation of Automatic Control) Copyright © IFAC 322 Hosting by Elsevier Ltd. All rights reserved. Copyright 2019 IFAC 322 Control. Peer review© responsibility of International Federation of Automatic Copyright © under 2019 IFAC 322 Copyright © 2019 IFAC 322 10.1016/j.ifacol.2019.09.052 Copyright © 2019 IFAC 322

Natural frequency [Hz]

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0.15

influence of the tire dynamics on the vibrations. In electric mode, the combustion engine and the flywheel are not attached to the drivetrain. Therefore, two main sources of non-linearity are eliminated in this set-up in order to emphasize the role of the tires. Tests have been performed in various driving situations. This paper is a basis for a comparative study on the ability of the most popular models from literature to simulate drivability relevant vibrations in passenger cars and gives a guidance for control engineers for the selection of models for their individual purpose, such as control design, parametrization or validation. In section 2, the experimental set-up is described. In section 3 the analysis methods are explained and the experimental analysis is performed. Based on these results a linear parameter varying model (LPV) is proposed in section 4. Section 5 concludes the findings.

0.10

2. EXPERIMENTAL SET-UP

11.8

Dry asphalt

Wet asphalt

11.6 11.4 11.2 11 0

20

40 60 Velocity [km/h]

80

100

(a) Trend of natural frequency.

Damping ratio

323

0.20

0.05 0

20

40 60 Velocity [km/h]

80

100

(b) Trend of damping factor.

Fig. 1. Vibration behavior at slip-free state of an electric vehicle, adapted from Yeap and M¨ uller (2016). lumped torsional spring/damper (still neglecting tire slip, but including the effect of torsional compliance) (Couderc et al. (1998); Bovee and Rizzoni (2016)) and to tire models including steady-state slip properties (Yeap and M¨ uller (2016); Rabeih and Crolla (1996)). This type of model cannot capture transient processes in the tire response. Therefore, the authors of (Bartram et al. (2010)) classify these models as not appropriate for dynamic maneuvers, such as pull-away (Tip-In at stand-still). These authors suggest using a so-called Rigid-Ring model, where the belt dynamics are handled by a torsional spring, which is coupled to the ground via a steady-state traction-slip relation. However, no experimental validation is given. Other research shows that the damping property of automotive drivetrains results from the velocity dependent tire slip. Those findings are based on either the model-based extrapolation of locally identified models (Fan (1994)), simulations (Rosenberger et al. (2011)), or pure theoretical approaches (Yeap and M¨ uller (2016)). The latter work predicts a strong dependency of the linearized system behavior on the vehicle speed (cf. Fig. 1), but only a qualitative experimental validation is done for two single maneuvers. This lack of a reliable and validated model could be one of the reasons, why comfort functions are still fully parametrized by cost-intensive test-drives. With the increasing importance of hybrid electric vehicles in the market, the parametrization of the drivetrain control functions gets even more laborious, as long as no model-based approaches are used. As a first step towards a reliable model, the system behavior is analyzed experimentally in a wide range of operating points. For that purpose, an experimental set-up has been built based on a plug-in electric vehicle (PHEV). The objective of these experiments is to validate the theoretical findings in Yeap and M¨ uller (2016) and to inspect the 323

A main objective of this research is to investigate the role of the tire on longitudinal vehicle vibrations after Tip-In. The experiments had to be performed in driving tests as test-rigs often induce additional dynamics, which perturb the result (G¨otting and De Doncker (2004)). A series production PHEV has been operated in electric mode and was equipped with additional sensors. 2.1 Hardware The engine control unit (ECU) of the series production car has been manipulated with an internal bypass in order to command a driving torque to the electric machine (EM) without any high-level filtering. The actual torque is estimated from measured electric quantities 1 and is recorded from the vehicle controller area network (CAN). The rotational speed of the EM and the wheels has been recorded from the vehicle CAN as well. For a better signal quality, analog resolvers have been used to capture the driven wheel speed. The front-wheel forces and torques have been obtained from piezo-electric measurement rims. The longitudinal acceleration and the rotational velocity of the car body were measured by an inertial measurement unit (IMU), mounted on the co-driver seat rail. More details on the sensor properties can be found in Table 1. 2.2 Signal Processing The measured quantities have been recorded with the minimal possible sampling time on two devices. Hence, a synchronization of the signals was necessary. The motor speed has been recorded on both devices and was used to synchronize the measurement data. Analog signals have been filtered by a analog Anti-Aliasing filter of 50 Hz before being sampled and recorded. The measurement data have been resampled to a 10 ms sampling time by shape-preserving piecewise cubic interpolation. For system identification, the signals have been filtered by a digital bilinear transformed low-pass Bessel filter with cutoff frequency at 10 Hz. This frequency is the threshold, until which humans perceive whole-body vibrations (cf. ISO 1 This estimator is in series production cars and is therefore confidential. Hence, no details can be given.

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Table 1. Properties of the measurement equipment. Quantity

Sensor

Type

Sampling Time

Datasheet

Wheel Force Wheel Torque ADC Acceleration Pitch Velocity EM speed Driven wheel angle Non-driven wheel speed

Kistler P625 Kistler P625 dSpace µ-Autobox 2 xSens MTi 10 xSens MTi 10 built-in Kistler P625 built-in

Piezoelectric Piezoelectric MEMS MEMS Incremental encoder Resolver Incremental encoder

analog analog 1ms 5ms 5ms 2ms analog 10ms

Kistler AG (2010, 2012) Kistler AG (2010, 2012) dSpace GmbH (2016) Xsens (2014) Xsens (2014) Kistler AG (2010, 2012) -

2631 (1997); ISO 8041 (2005)). The main advantages of the Bessel-Filter are the constant magnitude below the cutoff frequency and the constant group-delay, which preserves the time domain shape of the signal ((Raut and Swamy, 2010, p. 75)). All signal offsets have been removed for the identification procedure. An exception to this procedure is the derivation of the driven wheel speed. The resolver output is the wheel angle, given by its sine value Sin and its cosine value Cos. The rotational wheel speed ωw is then given by:   Sin , (1) ϕw = atan Cos d d (2) ωw = ϕ˙ w = Cos · (Sin) − Sin · (Cos). dt dt This representation avoids division by zero, when Cos is becoming zero. Furthermore, disturbances from numerical differentiation are reduced by the shown fusion of the derivatives of the original signals. Nevertheless, the resulting signal is additionally filtered by the described low-pass filter using zero-phase filtering. 2.3 Experiment design In Yeap and M¨ uller (2016), a notable variation of the natural frequency and the damping is predicted (c.f. Fig. 1). These properties are the result of a local linearization at distinct operating points, characterized by slip and velocity. There are two main challenges in the experimental validation of these findings: • It is difficult to guarantee specific slip conditions during a driving maneuver. • The traversing of backlash in the transmission system during driving maneuvers is inducing additional disturbances. In order to avoid backlash traversing, it is common practice to use an input offset in order to ensure the gears to stay in contact. However, this is constantly accelerating the vehicle and an operation point cannot be held. For an experimental analysis of the dynamic behavior at distinct operation points, step sequences of EM torque have been performed. • The sequence starts from a positive motor torque offset in order to prevent backlash traversing. • An identical torque sequence ensures similar slip conditions for repeated maneuvers. As the major amplitudes of the vibration are occurring during the first two periods, the vehicle speed is approximately constant during that time. Hence, the described maneuver is suitable for the investigation of the dynamic 324

behavior at distinct speed levels and low slip conditions. The analysis of these experiments are presented in section 3.2. The velocity range of the vehicle in a certain gear was limited by the relative speed of the two sides of the opened separation clutch of the combustion engine. On the other hand, the limited EM power restricts the use of extremely low gear ratios during the experiments. The third Gear is a trade-off between a large velocity range and a good system excitation and has been chosen for the investigation of the speed dependency of the system properties. The first gear one has been chosen to detect a possible influence of motorsided effects. 3. EXPERIMENTAL ANALYSIS In Yeap and M¨ uller (2016), a relationship of the dominant natural frequency of the system and its damping ratio was derived theoretically. For an experimental analysis of these dynamic properties step-sequences have been performed. The dominant vibration of the system response to these step-like excitation defines the second-order characteristics of the system. 3.1 Analysis method In order to guarantee a least-squares optimality of the estimated system characteristics, a second order system has been estimated with a Refined Instrumental Variable for Continuous-time Systems (RIVC) algorithm 2 . k Tm , ω m

Tr , ω w Jw

Jm

d

Fig. 2. Illustration of the two-inertias model Neglecting backlash and assuming ideally rolling wheels (cf. Alt et al. (2011); Grotjahn et al. (2006)), a linear transfer matrix can be determined from the ’two-inertias model’, illustrated in Fig. 2. This model reduces the drivetrain to two inertias (motor-sided inertia Jm and wheel-sided inertia Jw ) coupled by a viscously damped elasticity (damping factor d and spring stiffness k). The 2 The CONTSID Toolbox has been used and can be downloaded from http://www.cran.uhp-nancy.fr/contsid/. Details on the algorithm can be found in Young (2011)

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physical properties Tˆm , ω ˆ m and Jˆm are transformed to equivalent values in a system without gear ratios. Taking the overall gear ratio of the drivetrain igear into account the model parameters can be determined by 1 Tm = igear Tˆm , ωm = ω ˆ m , Jm = i2gears Jˆm (3) igears



 Jw (d s + k)  Jm Jw s2 + (Jm + Jw )d s + (Jm + Jw )k      Jw   (d s + k) r    J J s2 + (J + J )d s + (J + J )k  m w m w  m w  = G(s) =    Jw s    Jm Jw s2 + (Jm + Jw )d s + (Jm + Jw )k      Jw   (d s + k) mr   2 Jm Jw s + (Jm + Jw )d s + (Jm + Jw )k   b11 s + b10  a2 s 2 + a1 s + a0      b21 s + b20    a s2 + a s + a   2 1 0   (5) =   b31 s + b30    a2 s 2 + a1 s + a0      b41 s + b40   a2 s 2 + a1 s + a0

The full system equations can be found in Grotjahn et al. (2006). Here, the non-physical coefficients ai and bi are determined. The parameter b30 is estimated, because, the used estimation method doesn’t allow to use a priori knowledge about the location of poles or zeros. Although the transfer paths share the same poles, the coefficients are estimated separately during this analysis in order to show the statistical variation due to different measurement principles. Outliers with less then 70% NRMSF have been removed. The normalized root mean square fit (NRMSF) of a model output yˆ to the reference data y is defined as follows: 325

88

90

92 94 NRMSF [%]

96

98

100

Natural frequency [Hz]

(a) Statistical model fit for all step responses in third gear.

7.6 7.4 7.2 10

30

60 Velocity [km/h]

80 90 100

(b) Velocity trend of the natural frequency.

Damping ratio [-]

The path between the motor torque and the rotational speed of the motor ωm has integrating behavior. It is difficult to estimate that kind of transfer paths, because small perturbations, such as road elevation or wind influence, lead to drifts and seasonal variations in the signal which have to be removed for identification (Ljung, 1999, p. 459). The transfer path to the wheel speed ωw has integrating behavior, as well. In order to characterize the rotational motion of the drive-train, the torsional speed of the driveline ϑ˙ is used instead. The torsional speed is the difference of the rotational speed of the motor and the wheels ϑ˙ = ωw − ωm . (4) An advantage of this method is a better signal to noise ratio in comparison to other methods, where derivatives or high-pass filtering is needed. Together with the longitudinal acceleration ax , the wheel torque Tw and the longitudinal wheel force Fx , the output is chosen to be  T y = Tw Fx ϑ˙ ax . With input Tm , the transfer matrix can be given:

86

325

0.15 0.10 0.05 10

30

60 Velocity [km/h]

80 90 100

(c) Velocity trend of the damping factor.

Fig. 3. Dependency of a of 25 Nm to 185 Nm step response on the velocity in the third gear on dry asphalt (16 repeated maneuvers).  N ˆ[n])2 n=1 (y[n] − y . (6) NRMSF = 1 −  N 2 (y[n] − mean (y)) n=1

3.2 Analysis of experiments

Fig. 3 shows the distribution of dynamic properties of the estimated models for 16 repeated measurements of km maneuver A in the velocity range of 10 km h to 100 h in the third gear. As all transfer paths share the same poles, the natural frequency and the damping ratio are shown for all transfer paths in one plot. The vibrational characteristics have been plotted in box plots. The plots show the median, the quartiles and the 5% and the 95% quantile (the whiskers) of the results of all repetitions of an experiment. Fig. 3(a) shows, the estimation quality of the method. The whiskers of the NRMSF are between approximately 87 % and 95 %. This shows that the method leads to a good model fit. Hence, the system has linear second-order behavior at distinct operation points. Furthermore, it can be seen that the natural frequency is in the range of approximately 7.1 Hz to 7.7 Hz. This is considerably lower than the values in Fig. 1. The reason is that Yeap and M¨ uller (2016) investigates individual wheel drives. In addition, it is known that the natural

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Natural frequency [Hz]

Natural frequency [Hz]

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3.45

3.4

0

20 Velocity [km/h]

3.4 3.2

40

40

65 90 Step height [Nm]

115

(a) Trend of the natural frequency with increasing step height in gear one.

Damping ratio [-]

(a) Velocity trend of the natural frequency on dry (black) and wet asphalt (red).

Damping ratio [-]

3.6

0.12 0.10 0.08 0.06

0.15 0.10 0.05

0.04 0

20 Velocity [km/h]

40

40

65 90 Step height [Nm]

115

(b) Velocity trend of the damping factor on dry (black) and wet asphalt (red).

(b) Trend of the damping ratio with increasing step height in gear one.

Fig. 4. Comparison of 10 Nm to 75 Nm step responses on dry asphalt (black, 8 repeated maneuvers) and on wet asphalt (red, 4 repeated maneuvers) in the first gear.

Fig. 5. Trend of the system properties with increasing step height for velocities between 0 km/h and 40 km/h on dry asphalt in the first gear (43 step experiments).

frequency of the drivetrain is increasing with lower gear ratios. A natural frequency between 2 Hz and 10 Hz is often reported for conventional driveline topologies (c.f. e.g. Sorniotti (2008)). With increasing velocity, the median of the estimated natural frequency of the system is increasing about 0.2 Hz (being 3% of the initial value at 10 km/h. This is matching to the theoretical prediction in Yeap and M¨ uller (2016). However, in comparison to the variation of the estimated natural frequency for one operating point, the trend is rather weak. Comparing Fig. 3(c) and Fig. 1(b), it can be seen that the damping ratio is on the same level. Moreover, in Fig. 3(c), the damping ratio is increasing approximately by 0.1 (being 200% of the initial value at 10 km/h). This is matching the theoretical approach in 1(b) again. In contrast to the results of the natural frequency, this trend is strong in comparison to the variation of the results in one operating point. Furthermore, Yeap and M¨ uller (2016) predict a remarkable dependency of the system properties on the road conditions (c.f. Fig. 1). Fig. 4 shows a comparison of the estimated system properties for maneuvers on wet and dry asphalt in the first gear. In this gear, the velocity range is restricted to 0 km/h to 40 km/h, because of the motor speed limitation. As expected, the natural frequency is clearly lower, than in the third gear. However, there is no significant difference between the results on wet and on dry asphalt. The natural frequency is approximately between 3.35 Hz to 3.5 Hz for both road conditions and is almost constant over the entire velocity range. In addition, there is no difference in the damping property (Fig. 4(b)) between the results of the different road conditions. However, it can be seen that the values damping ratio are almost identical 326

in gear one and three. Consequently, it can be assumed that the main damping occurs on the wheel-side of the drivetrain. In addition to the vehicle speed, the excitation height is another external factor that reveals a nonlinear behavior of a system. Fig. 5 shows the dependency of the system properties on the step height in the first gear. The median of the natural frequency is rising almost proportional to the step height (c.f. Fig. 5(a)). The variation is rather low in comparison to the observed trend. Exceptions are the results from experiments with a step height of 40 Nm, where the lower whisker length is almost 0.2 Hz. This exceptional high variation occurs in the results of the damping as well. A reason could be that for weak excitations, nonlinear speed-dependent friction effects are dominant in the system dynamics. Furthermore, the results show that the median of the damping is approximately constant for all step heights. This shows once again that the damping ratio is almost independent of influences from the motor-side. 4. LINEAR PARAMETER VARYING MODEL The previously described analysis showed that the damping behavior is strongly depending on the vehicle speed while the variation of the natural frequency is rather not deterministic. This is why a linear parameter varying (LPV) model with varying damping ratio D(v) is introduced here. With the definition of the natural frequency ω0 w) ω02 = k (JJmm+J Jw , the damping ratio D(v) = d(v) 2 k , the characteristic polynomial p(s) = ω12 s2 + 2D ω0 s + 1 and numerato n(s) = to

D ω0

0

s + 1, model (5) can be reformulated

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K4 [(kg/m)−1 ]

4.50

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·10−6

4.00

3.50 10

30

60 Velocity [km/h]

80 90 100

Fig. 6. Example of a typical velocity behavior for Ki using K4 as an example (output signal ax ) in third gear. 

GT (s) = k n (s) Jm ω02

k n (s) Jm r ω02

p(s)

p(s)



1 Jm ω02

p(s)

s

k n (s) Jm m r ω02

p(s)

K1 n (s) K2 n (s) K3 s K4 n (s) ω02 p(s) ω02 p(s) ω02 p(s) ω02 p(s)





= (7)

.

Fig. 6 shows a typical velocity behavior of the parameters K1 , K2 and K4 using K4 as an example. It validates that these parameters are indeed constant in the operating range. Hence, only the damping ratio D(v(t)) is a function of the vehicle speed v(t). An LPV system can be stated with time-varying parameter v(t). However, most LPV control methods need a canonical transfer state-space representation of the system (c.f. Shamma (2012)). Therefore, this strictly proper transfer matrix (with u = Tm and T  y = Tw Fx ϑ˙ ax ) is transformed to the controllable canonical form:     0 1 0 x˙ = x + u, (8) 1 −ω02 −2 D(v(t)) ω0  T K1 K2 K3 K4 y = D(v(t)) K1 D(v(t)) K2 x. (9) K4 0 D(v(t)) ω0 ω0 ω0 There are several possibilities to account for the parameter variation during the LPV control design. For example, the medians of the system characteristics can be used directly or a polynomial, fitted to the experimental results, can be used. Additionally, it is noted here that with the chosen output, the two-inertias model, as it is stated in Grotjahn et al. (2006), is not fully observable. This is the reason why the proposed LPV model is of second order, while the model in Grotjahn et al. (2006) is of third order. 5. CONCLUSION AND IMPLICATIONS FOR SYSTEM MODELING In this work, an experimental analysis of the shuffle phenomenon has been performed and the dependency on velocity, motor torque step-height and road conditions has been quantified. First of all, it can be stated that second order models fit the step experiments very good at specific operating points. This is in line with the popularity of the linear ’two-inertias model’. Furthermore, the strong velocity dependency of the damping ratio, predicted in Yeap and M¨ uller (2016), has been 327

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experimentally confirmed. Consequently, nonlinear models or quasi-linear approaches are needed to capture this effect. It was also shown that the damping is mainly affected by effects occurring at the wheel-side of the drivetrain. In contrast, the trend of a rising natural frequency with increasing velocity is observed with high variation in the estimation results in relation to the strength of the trend. A linear dependency of the natural frequency on the step height has been observed, but it is rather weak in comparison the variation of the estimated natural frequency over all experiments. Furthermore, no significant dependency of the driveline shuffle on normal road condition variations has been observed. All in all, the experiments match qualitatively the theoretical result in Fig. 1. However, the theoretical results overemphasize the role of the road conditions and the impact of the vehicle speed on the natural frequency. To sum up, there is a strong dependency of the damping ration on the vehicle speed, but no significant deterministic trend of the natural frequency has been found. This is why an LPV model has been proposed in section 4. However, the validation for other test signals and a comparison to other models needs to be done in future publications. In any case, the physical model of Yeap and M¨ uller (2016) cannot be validated quantitatively without individual parameters for the used test car. These can be obtained by parameter identification with suitable test signals for the frequency range of interest and will be done in future publications. Moreover, in order to generalize the results, an additional analysis of further tests in other passenger cars are needed. Nevertheless, the results are an indicator of the behavior of passenger cars in a wide range of operating points. Therefore, the results are a base for quantitative validation of models in wide range of operating points for control design and validation. In future publications, these findings will be used to validate the model of Yeap and M¨ uller (2016) and to compare it to other popular models. ACKNOWLEDGEMENTS Thanks to Florian Brunner for support in ECU-Bypass Coding, Sven Dannenberg for support in transmission control and Andreas Daasch and Dieter Schwarzmann for the provision of a test vehicle. REFERENCES Alt, B., Antritter, F., Svaricek, F., Wobbe, F., B¨ ohme, T., and Schultalbers, D.M. (2011). Two Degree of Freedom Structure for Reduction of Driveline Oscillations. In AUTOREG, 361–374. VDI, Baden-Baden. Angeringer, U. and Horn, M. (2011). Sliding mode drive line control for an electrically driven vehicle. In International Conference on Control Applications (CCA), 521– 526. IEEE, Denver. doi:10.1109/CCA.2011.6044416. Bartram, M., Mavros, G., and Biggs, S. (2010). A study on the effect of road friction on driveline vibrations. Journal of Multi-body Dynamics, 224(4), 321–340. doi: 10.1243/14644193JMBD266. Baumann, J., Torkzadeh, D.D., Ramstein, A., Kiencke, U., and Schlegl, T. (2006). Model-based predictive anti-jerk control. Control Engineering Practice, 14(3), 259–266. doi:10.1016/j.conengprac.2005.03.026.

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